Question

Решить систему уравнений: 3x2-2xy+y2=6 x-2y=3

Answer 1

3х^2 - 2xy + y^2 = 6 x - 2y = 3 x = 2y + 3 3( 2y + 3 )^2 - 2y( 2y + 3 ) + y^2 = 6 3( 4y^2 + 12y + 9 ) - 4y^2 - 6y + y^2 = 6 12y^2 + 36y + 27 - 4y^2 - 6y + y^2 - 6 = 0 9y^2 + 30y + 21 = 0 3( 3y^2 + 10y + 7 ) = 0 d = 100 - 84 = 16 = 4^2 y1 = ( - 10 + 4 ) : 6 = - 1 y2 = ( - 10 - 4 ) : 6 = - 7/3 = - 2 1/3 x = 2y + 3 x1 = 2•( - 1 ) + 3 = 1 x2 = 2•( - 7/3 ) + 3 = - 14/3 + 3 = - 4 2/3 + 3 = - 1 2/3 ответ ( 1 ; - 1 ) ; ( - 1 2/3 ; - 2 1/3 )